Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry

Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. We find that: (i) The best-performing VQEs require gate-error probabilities between 10⁻⁶ and 10⁻⁴ (10⁻⁴ and 10⁻² with error mitigation) to predict, within chemical accuracy, ground-state energies of small molecules with 4 − 14 orbitals. (ii) ADAPT-VQEs that construct ansatz circuits iteratively outperform fixed-circuit VQEs. (iii) ADAPT-VQEs perform better with circuits constructed from gate-efficient rather than physically-motivated elements. (iv) The maximally-allowed gate-error probability, p_c, for any VQE to achieve chemical accuracy decreases with the number N_II of noisy two-qubit gates as \({p}_{c}\mathop{\propto }\limits_{\displaystyle{ \sim }}{N}_{{{{\rm{II}}}}}^{-1}\) $p_c\underset{~}{\propto }{N}_{\mathrm{II}}^{-1}$ . Additionally, p_c decreases with system size, even with error mitigation, implying that larger molecules require even lower gate-errors. Thus, quantum advantage via gate-based VQEs is unlikely unless gate-error probabilities are decreased by orders of magnitude.